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A333064 Number of entries in the seventh blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

%I A333064 #5 Mar 06 2020 19:40:56
%S A333064 1,29,499,6676,77078,810470,8016373,76334142,713507667,6658565009,
%T A333064 62882380589,606149817728,5983648334738,60440402586898,
%U A333064 622934996801505,6532386995235676,69575530733726891,752420279343383619,8269751757387345271,92538014365261646366
%N A333064 Number of entries in the seventh blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.
%H A333064 Alois P. Heinz, <a href="/A333064/b333064.txt">Table of n, a(n) for n = 7..576</a>
%H A333064 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A333064 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A333064       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
%p A333064        combinat[multinomial](n, i$j, n-i*j)/j!*
%p A333064       b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
%p A333064     end:
%p A333064 a:= n-> b(n$2, 7)[2]:
%p A333064 seq(a(n), n=7..26);
%Y A333064 Column k=7 of A319375.
%K A333064 nonn
%O A333064 7,2
%A A333064 _Alois P. Heinz_, Mar 06 2020